What is the Ground State Energy of 12 Neutrons in a 1D Infinite Square Well?

[roeb]

Homework Statement

Twelve nucleons are in a one dimensional infinite square well of length L = 3 fm. Using a mass of 1 u. What is the ground state energy of the system of 12 nucleons in the well if all the nucleons are neutrons so that there can only be 2 in each state.

Homework Equations

The Attempt at a Solution

E = n^2 h^2 / ( 8 m L^2) (infinite square well)

I'm not really sure what to do... If I say that n = 1. Then I get 22.96 MeV.
I know that because of the exclusion principle there will be levels from n = 1 to n = 6 with 2 neutrons in each level.

I don't know exactly what they mean by ground state? I would have thought that means when n = 1, but in this case it doesn't seem to be the case. Or even 22.96 Mev / 12 nucleons, but that also isn't the answer.

 

[Domnu]

Well, neutrons are fermions, so n can't only be 1 (Pauli exclusion principle). There have to be two neutrons in n = 1, two in n = 2, ... n = 6. Try working from here.